11.4 Invasive and Non-Invasive Hemodynamic and Respiratory Monitoring

11.4 Invasive and Non-Invasive Hemodynamic and Respiratory Monitoring

Clinical monitoring in anaesthesia translates physical phenomena—optical light absorption, infrared spectral attenuation, hydraulic pressure transduction, and microvoltage neuro-electric potentials—into quantitative physiological metrics. Understanding the physical principles, dynamic response characteristics, and artifact etiologies of clinical monitors is essential to maintain patient safety.

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Pulse Oximetry: Spectrophotometry and Optical Plethysmography

Pulse oximetry provides non-invasive, continuous measurement of arterial hemoglobin oxygen saturation ($SpO_2$) by combining two physical techniques: spectrophotometry (measuring light absorption across specific wavelengths) and optical plethysmography (identifying pulsatile vascular volume changes).

The Beer-Lambert Law

Optical absorption follows the Beer-Lambert Law: $I = I_0 e^{-\epsilon(\lambda) c d} \quad \implies \quad A = \log_{10}\left(\frac{I_0}{I}\right) = \epsilon(\lambda) \cdot c \cdot d$ where:

• $I_0$ = incident light intensity
• $I$ = transmitted light intensity
• $A$ = total optical absorbance
• $\epsilon(\lambda)$ = extinction coefficient of the absorbing substance at wavelength $\lambda$
• $c$ = concentration of the absorbing substance
• $d$ = optical path length through the tissue

Dual-Wavelength Measurement Physics

Pulse oximeter probes contain two miniature light-emitting diodes (LEDs) and a single photodiode detector:

1. Red Light ($660\text{ nm}$): Deoxygenated hemoglobin ($Hb$) has an extinction coefficient approximately $10$ times higher than oxygenated hemoglobin ($HbO_2$). Therefore, deoxygenated blood strongly absorbs $660\text{ nm}$ red light.
2. Infrared Light ($940\text{ nm}$): Oxygenated hemoglobin ($HbO_2$) has a higher extinction coefficient than deoxygenated hemoglobin ($Hb$). Therefore, oxygenated blood absorbs $940\text{ nm}$ infrared light more avidly.

• The Isobestic Point: A wavelength where two chemical species possess identical extinction coefficients (e.g., $590\text{ nm}$ and $805\text{ nm}$ for $Hb$ and $HbO_2$). At an isobestic point, light absorption depends strictly on total hemoglobin concentration, independent of oxygen saturation.

Photoplethysmography and the "Ratio of Ratios"

To isolate arterial blood from non-arterial absorbers, the oximeter separates the detected photoplethysmographic signal into two components:

• AC Component (Pulsatile): Caused by systolic arterial pulsation expanding the arteriolar vascular bed, rhythmically modulating optical path length ($d$).
• DC Component (Non-Pulsatile / Baseline): Constant light attenuation by venous blood, capillary beds, connective tissue, bone, and skin pigments.

The monitor calculates the dimensionless Ratio of Ratios ($R$): $R = \frac{AC_{660} / DC_{660}}{AC_{940} / DC_{940}}$

• Calibration Curve: Because tissue scattering prevents direct mathematical calculation from Beer-Lambert equations, microprocessors map $R$ against an empirical calibration curve obtained from healthy human volunteers:
  • $R = 0.4 \implies SpO_2 = 100\%$
  • $R = 1.0 \implies SpO_2 = 85\%$
  • Volunteers cannot safely be desaturated much below about $70-75\%$, so readings below that range are extrapolated and less accurate.

Dyshemoglobinemias and Artifacts

1. Carboxyhemoglobin ($COHb$): $COHb$ absorbs light at $660\text{ nm}$ with an extinction coefficient virtually identical to $HbO_2$, while absorbing minimally at $940\text{ nm}$. Standard two-wavelength pulse oximeters cannot distinguish $COHb$ from $HbO_2$. The monitor counts $COHb$ as $HbO_2$, displaying a falsely normal or elevated $SpO_2$ (e.g., reading $98\%$ when true arterial fractional saturation $SaO_2$ is $65\%$). Accurate diagnosis requires multi-wavelength co-oximetry.
2. Methemoglobinemia ($MetHb$, Ferric $Fe^{3+}$ Iron): $MetHb$ exhibits very high and virtually identical extinction coefficients at both $660\text{ nm}$ and $940\text{ nm}$. As $MetHb$ concentrations exceed $20-30\%$, the ratio $R$ is mathematically forced toward $1.0$. Looking at the calibration curve, $R = 1.0$ corresponds to an $SpO_2$ locked at approximately $85\%$, regardless of true arterial oxygenation (underestimating true saturation if $SaO_2 > 85\%$, overestimating if $SaO_2 < 85\%$).
3. Intravenous Dyes:
   • Methylene Blue: Optical absorption peak at $668\text{ nm}$ (closely matching the red LED). Induces a precipitous, false drop in $SpO_2$ to $60-65\%$ lasting several minutes.
   • Indocyanine Green and Indigo Carmine: Induce minor, transient false drops in $SpO_2$.
4. Physiological Limitations: Severe hypoperfusion (hypovolemic shock, severe vasoconstriction, hypothermia, low cardiac output) diminishes pulsatile $AC$ amplitude below the signal-to-noise detection threshold. Venous pulsations (severe tricuspid regurgitation, tight probe application) introduce an $AC$ signal into venous blood, causing false underestimation of $SpO_2$.

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Infrared Capnography: Physics and Waveform Morphology

Capnography provides continuous, real-time monitoring of carbon dioxide concentration in respiratory gases.

Physical Measurement Principle: NDIR Spectroscopy

Capnometers utilize Non-Dispersive Infrared (NDIR) Spectroscopy. Asymmetrical polyatomic gas molecules absorb specific wavelengths of infrared radiation through rotational-vibrational excitation. The carbon dioxide molecule ($O=C=O$) absorbs infrared radiation strongly at a narrow absorption band of $4.26\text{ }\mu\text{m}$ (with zero absorption by symmetrical diatomic molecules like $O_2$ and $N_2$). Transmitted IR energy is converted into a $P_{CO_2}$ value via Beer-Lambert kinetics.

Mainstream vs. Sidestream Analyzers

• Mainstream (In-Line): The sensor cell is placed directly at the airway between the ETT and breathing circuit.
  • Advantages: Instantaneous response time ($<50\text{ ms}$), zero transit delay, no scavenging required.
  • Disadvantages: Adds mechanical dead space ($5-10\text{ mL}$), heavy at the airway (risking accidental extubation), optical windows prone to condensation and mucus contamination, heated sensor ($41-42°\text{C}$) risks thermal skin burns.
• Sidestream (Diverting): Continuously aspirates gas from the airway connector via a fine capillary sampling tube at $150\text{ to }200\text{ mL/min}$ to an internal analyzer in the monitor.
  • Advantages: Minimal weight at the airway, compatible with awake/non-intubated patients via nasal prongs.
  • Disadvantages: Transit time delay of $1-3\text{ seconds}$, waveform dispersion/blunting along sampling tubing, water trap obstruction by condensation.

The Normal Capnogram Waveform

  PCO2
  (mmHg)         Phase III (Alveolar Plateau)
   40 |                  /------------------* (ETCO2)
      |                 /                   |
      |   Phase II     /                    | Phase 0
      |  (Upstroke)   /                     | (Inspiratory Downstroke)
      |              /                      |
    0 +-------------/                       +-----------------
        Phase I (Baseline)                     Phase I (Next Breath)

1. Phase I (Inspiratory Baseline): Exhalation of gas from anatomical dead space containing zero $CO_2$ ($P_{CO_2} = 0\text{ mmHg}$). Baseline must touch zero.
2. Phase II (Expiratory Upstroke): Rapid upstroke representing transitional mixing of $CO_2$-free anatomical dead space gas with early alveolar gas.
3. Phase III (Alveolar Plateau): Exhalation of alveolar gas from across lung units. Slopes gently upward because slow-emptying alveoli have lower ventilation-perfusion ($V/Q$) ratios and higher $P_{CO_2}$. The peak value at the very end of expiration is the End-Tidal $CO_2$ ($ETCO_2$).
4. Phase 0 (Inspiratory Downstroke): Rapid, steep descent back to zero as fresh, $CO_2$-free gas is inhaled.

Alveolar-to-Arterial $CO_2$ Gradient

Under normal physiological conditions, end-tidal $CO_2$ is slightly lower than arterial $P_a CO_2$: $P_a CO_2 - ETCO_2 \approx 2-5\text{ mmHg} \quad (0.3-0.7\text{ kPa})$ This gradient is caused by normal alveolar dead space ($V_D / V_T$)—alveoli that are ventilated but under-perfused ($V/Q \rightarrow \infty$), diluting alveolar gas with $0\text{ mmHg } CO_2$.

• Pathological Widening of the Gradient: Any condition that increases alveolar dead space widens the $P_a CO_2 - ETCO_2$ gradient, causing $ETCO_2$ to plummet relative to $P_a CO_2$:
  • Pulmonary thromboembolism or air embolism
  • Severe hypovolemia, hemorrhage, or acute cardiac arrest (loss of pulmonary perfusion)
  • Excessive positive end-expiratory pressure (PEEP) overdistending non-dependent alveoli
  • Chronic obstructive pulmonary disease (COPD)

Pathological Capnography Waveforms

1. Bronchospasm / Obstructive Airway Disease: Prolonged, sloped Phase II and steep upward-sloping Phase III, producing the classic "shark-fin" appearance. Caused by heterogeneous airway narrowing and prolonged expiratory time constants across obstructed lung units.
2. Rebreathing of Carbon Dioxide: Elevation of the Phase I baseline ($>0\text{ mmHg}$). Caused by an exhausted soda lime canister, channeling within the absorbent, or an incompetent expiratory unidirectional valve in a circle system.
3. Curare Cleft: A distinct dip or notch in the final third of the Phase III alveolar plateau, representing brief spontaneous diaphragmatic contraction against the ventilator as neuromuscular blockade wears off.
4. Cardiogenic Oscillations: Small, rhythmic ripples on Phase III and Phase 0, caused by the mechanical pulsation of the heart displacing gas within adjacent lung segments during low respiratory rates.
5. Sudden Loss of $ETCO_2$ to Zero: Immediate diagnostic emergency indicating circuit disconnection, accidental tracheal extubation, complete airway obstruction, esophageal intubation, or cardiac arrest.

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Invasive Arterial Blood Pressure (IABP) Monitoring

Invasive arterial catheterization provides beat-to-beat blood pressure tracking and arterial blood gas sampling.

Transducer Physical Architecture

The system comprises an intra-arterial cannula, fluid-filled non-compliant tubing, stopcocks, a continuous flush device ($3-4\text{ mL/hr}$ heparinized saline pressurized to $300\text{ mmHg}$), and a piezoresistive strain gauge transducer.

• Piezoresistive Transduction: Hydraulic pressure pulses flex a silicon diaphragm embedded with a Wheatstone bridge circuit. Microscopic deformation alters electrical resistance, converting physical pressure into an electrical voltage signal proportional to arterial pressure.

Dynamic Response: Natural Frequency and Damping

The fluid-filled catheter-tubing-transducer assembly is a mechanical harmonic oscillator with distinct dynamic physical properties:

1. Natural Resonant Frequency ($f_n$): The frequency at which the system oscillates freely when perturbed. The arterial pressure wave consists of a fundamental frequency equal to the heart rate ($1-2\text{ Hz}$) plus multiple harmonic frequencies up to the 10th harmonic ($10-20\text{ Hz}$). To prevent resonant amplification, the system's natural frequency must be at least 5 times the fundamental frequency: clinically, $f_n > 25\text{ Hz}$ is mandatory.
2. Damping Coefficient ($\zeta$): Quantifies the viscous friction that opposes oscillation and absorbs energy from the pressure wave. Optimal damping is $\zeta = 0.64-0.70$ (adequate clinical range: $0.6-0.8$).

The Fast-Flush (Square-Wave) Test

Pulling and abruptly releasing the high-pressure flush valve sends a $300\text{ mmHg}$ square wave through the system, inducing free oscillation:

• $f_n$ Calculation: $f_n = \frac{\text{Paper/Sweep Speed (mm/s)}}{\text{Wavelength of one oscillation cycle (mm)}}$.
• Damping Ratio ($\zeta$): Calculated from the amplitude ratio of two consecutive oscillation peaks ($A_2 / A_1$).

Causes of Overdamping: Air bubbles in tubing/transducer (highly compressible air absorbs kinetic energy), blood clots, compliant tubing, excessive stopcocks, arterial kinking.

Hydrostatic Leveling and Pressure Offsets

The transducer must be zeroed and leveled to a standardized anatomical landmark:

• Standard Reference: The Phlebostatic Axis (4th intercostal space at the mid-axillary line, corresponding to the right atrium).
• Neurosurgical / Sitting Position: Leveled to the External Auditory Meatus (Tragus / Circle of Willis) to accurately quantify cerebral perfusion pressure ($CPP = MAP - ICP$).
• Hydrostatic Column Physics: $1\text{ cm } H_2O = 0.735\text{ mmHg} \approx 0.74\text{ mmHg} \quad (1\text{ mmHg} = 1.36\text{ cm } H_2O)$
  • If the transducer is positioned $10\text{ cm}$ BELOW the reference axis, hydrostatic pressure adds to the signal: blood pressure reads $7.4\text{ mmHg}$ falsely high.
  • If the transducer is positioned $10\text{ cm}$ ABOVE the reference axis, blood pressure reads $7.4\text{ mmHg}$ falsely low.

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Depth of Anaesthesia Monitoring: Processed EEG

Processed electroencephalography (EEG) monitors quantify cortical electrical activity to gauge the hypnotic component of general anaesthesia.

The Bispectral Index (BIS)

BIS processes frontal bipolar EEG signals through mathematical algorithms combining four sub-components: beta ratio (high frequency activity), synch fast slow (bispectral phase coupling), burst suppression ratio ($BSR$), and QUAZI suppression.

• BIS Numerical Scale (0 to 100):
  • $100$: Fully awake, alert
  • $60-80$: Sedated, conscious sedation
  • $40-60$: Target range for general anaesthesia (low probability of explicit recall)
  • $20-40$: Deep hypnotic state
  • $<20$: Burst suppression pattern
  • $0$: Completely isoelectric EEG (cortical electrical silence)

Paradoxical Readings and Clinical Pitfalls

1. Ketamine: Promotes high-frequency frontal beta and gamma oscillations ($25-40\text{ Hz}$), causing BIS values to paradoxically rise to $70-90$ despite deep surgical dissociative anaesthesia.
2. Nitrous Oxide: Produces fast cortical EEG patterns without altering BIS values significantly.
3. Hypothermia and Ischemia: Profound hypothermia ($<32°\text{C}$), severe hypotension, hypoglycemia, or cerebral ischemia reduce cortical metabolism, lowering BIS toward burst suppression independently of anaesthetic depth.
4. Electromyographic (EMG) Artifact: High-frequency scalp muscle shivering or electrical interference falsely elevates BIS values.

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Advanced Cardiac Output Monitoring

1. Pulmonary Artery Catheter (PAC) Thermodilution: A known volume ($V_i$) of cold saline is injected into the right atrium. A distal thermistor in the pulmonary artery records temperature change over time. Cardiac output is calculated via the Stewart-Hamilton Equation: $CO = \frac{V_i (T_b - T_i) \cdot K}{\int_0^\infty \Delta T_b(t) \, dt}$ The area under the thermodilution curve is inversely proportional to cardiac output: a low cardiac output produces a prolonged, tall curve (slow indicator clearance); a high cardiac output produces a small, narrow curve.
2. Pulse Contour Analysis (e.g., FloTrac, PiCCO): Derives stroke volume beat-to-beat by mathematical integration of the area under the systolic portion of the arterial pressure waveform, incorporating patient aortic compliance and systemic vascular resistance.
3. Transesophageal Echocardiography (TEE) and Doppler: Measures blood flow velocity across the aortic valve or descending aorta via Doppler shift, integrating velocity over time (Velocity-Time Integral, $VTI$) multiplied by aortic cross-sectional area to determine stroke volume ($SV = VTI \times \text{Area}$).

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Clinical Pearls and Exam Traps